Exercises 55-60
Exercise 61. Use the Cayley-Hamilton theorem
to compute eA, where
| a) | A = |  |
3 | -2 |  | , | | -1 | 4 | |
|
| |
| b) | A = |  |
0 | 1 | 0 | 0 |  | . |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | |
|
Answer
Exercise 62. Use the Cayley-Hamilton theorem
to compute the inverse of
| A = | 
| 1 | 0 | 0 |  |
| 0 | 1 | 1 |
| -2 | -2 | -1 |
|
from the characteristic equation of A.
Also calculate det (A).
An example
Answer
Exercise 63. Compute sin ((
/ 2) A), where
| A = |
| 1 | 4 | 9 | | . |
| 0 | -2 | 3 |
| 0 | 0 | -1 |
An example
Answer
Exercise 64. The eigenvalues of a 3 x 3 -matrix A
are
-2, 1 and 2. Moreover,
| A2 - A = |
| 6 | 0 | 0 | | . |
| 0 | 0 | 0 |
| 4 | 0 | 2 |
|
Find the inverse of A, the
determinant of A and sin (A -1).
An example
Answer
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